Old joke: Father O’Brien was driving home after lunch when a policeman pulled him over. “What have you been drinking?” asked the cop. “Only water,” replied the priest. “Then what’s that next to you?” said the policeman, pointing to the half-empty bottle of pinot noir in the passenger seat. “Good Lord!” said Father O’Brien. “He’s done it again!”

Father O’Brien was onto something. Drinking at work can be miraculous. Scientists at the University of Illinois at Chicago discovered that creativity increases 50% after a few drinks — and speeds up response times.

In a study published this year in the journal Consciousness and Cognition, psychologists gave their subjects enough vodka-and-cranberry to put their blood-alcohol at almost 0.08, which is the legal limit. Then the volunteers played a game in which they were given a group of words, such as peach, arm and tar, and asked to come up with another word that could be used in combination with any of the above, such as pit.

Tipplers delivered more correct answers and delivered them more quickly. Drinkers solved nine problems on average, versus six for the sober group, and came up with answers in an average of 11.5 seconds as against 15.2 for the teetotalers.

Twenty-five percent faster, 50% more creative? Don Draper, once again you have been proven right.

Psychologists have speculated that drinking may spur creativity because it decreases the ability to control your thoughts. In other words, the very reason we use alcohol in social situations — to lower the barriers — works on an intellectual plane as well.

The main problem with drinking at lunch is that there isn’t enough of it.

For once, society really is to blame. Order a midday Bloody Mary and your co-workers become Frowny Harrys. Here in the city, though, we aren’t driving home afterwards or, for the most part, operating heavy equipment. So the no-booze-at-lunch stance tends to be more moralistic than practical.

There is also a perception that drinking at lunch, or even dinner, is linked to lower intelligence. Another psychological study, this one to be published in the Journal of Consumer Psychology by Scott Rick of the University of Michigan and Maurice Schweitzer of Wharton Business School, discovered what they called an “imbibing idiot bias.” They found that, during job interviews over dinner, candidates who ordered a glass of wine were rated as less intelligent than non-drinkers by their dining companions.

Drinking didn’t seem to impair the mental agility of the late Christopher Hitchens, who consumed half a bottle of wine or so each midday, though he advised, “Try to eat something . . . at every meal.”

Drinking at lunch has long been opposed by Puritans, jihadists, miserable freaks in general and Jimmy Carter in particular. In 1976 Carter actually campaigned against “the three-martini lunch” before putting on a sweater and lecturing us about how depressed we all were (at least as long as he was president). His first lady bragged that she enjoyed seeing people “kind of squirm” when they learned no liquor was served in the Carter White House.

When Ibn Saud, the founder of Saudi Arabia, explained to Winston Churchill that his religion forbade smoking and drinking, Churchill said that for him it was “an absolutely sacred rite” to have “alcohol before, after, and if need be during all meals and in the intervals between them.”

We’ve got it all wrong at lunch these days, savoring our locally nurtured bean sprouts sprinkled with organic vinaigrette. No sprout that ever crept out of the ground (where, frankly, it should probably be left) tastes as good as a glass of cheap chardonnay, much less a Chateau Petrus.

Then there are the business reasons for drinking at lunch. It’s a power play. It shows confidence. It makes things happen.

Longtime Playboy drinking columnist Dan Dunn, author of “Living Loaded,” told BusinessWeek that a lunchtime tipple is “sending a very clear message that you’re not the kind of guy to be trifled with.” He added that enjoying a liquid lunch was “like sex” — “someone may find your proposal a lot more interesting after six or seven vodka tonics.”